
We assume that the sequences are circular, i.e. periodic boundaries:
\(x_{N+i}=x_{i},\forall i \in \lbrace 1,\ldots , N\rbrace \) .

We neglect the existence of coding sequences separated by non coding regions. Biologically, this corresponds to compact genomes with almost no non-coding sequences.
In this sense, our model mimics the molecular evolution of some viruses [1]} or (animal) mitochondrial DNA [2]}.
Consequently, we are modelling intragenic mutations[3]}, [4]}.

We neglect geometrical aspects such as physical configurations like folding, twists, coiled structures, hairpin loops, etc.

We do not consider transcription-translation processes.

We do not include recombination, so we are modelling asexual replication.

